In various communication systems, digital-to-analog converters are used to convert digital signals to analog signals before transmission. Digital-to-analog converters may introduce quantization noise into the analog signals—particularly when a large number of signal levels are used. Examples of techniques that utilize a large number of output levels include Tomlinson-Harashima-Precode and advance modulation schemes such as OFDM and discreet multi-tone modulation.
Typically, to reduce the effect of quantization noise on system performance, a power spectrum density (PSD) level of the quantization noise should be below a predetermined PSD level of unavoidable noises. A typical requirement is for the quantization noise to have a PSD that is 10 decibels below the PSD of unavoidable noises. Examples of unavoidable noises include additive white Gaussian noise (AWGN), alien cross-talk from other cables or transmitters and quantization noise of the analog to digital converter at the receiver.
Conventional digital-to-analog converter designs produce a quantization noise with a white PSD evenly distributed among all frequency components. However, the communication system performance is often limited by a worst case channel. The frequency response of this channel varies significantly within the transmission bandwidth. As a result, the quantization noise from the transmitter digital-to-analog converter may be shaped by the channel and observed by the receiver.
The peak of the quantization noise PSD (shaped by the channel) observed by the receiver must be lower than other noises by a predetermined level. As a result, a large number of bits may be required for the digital-to-analog converter input and the digital-to-analog converter size and complexity are increased. Reducing the size and complexity of a digital-to-analog converter would lower the overall cost of the system.
Referring now to FIG. 1, a transmitter 8 having an input 10 from an advance modulation scheme or a pre-coding scheme is illustrated. The input 10 generates an N-bit digital input to a truncation module 12. The truncation module 12 truncates the N-bit signal to an M-bit signal, where M is an integer less than N. The truncation module 12 eliminates the least significant bits from the N-bit digital input signal. The M-bit signal is provided to a digital-to-analog converter 14 where it is converted to an analog output signal corresponding to the M-bit signal.
Referring now to FIG. 2, a signal model illustrating the input signal an, which corresponds to the output of the truncation module 12, is summed with truncation noise qn at a summing module 16. The truncation noise qn is inherent in the truncation module 12. The truncation noise is sometimes referred to as quantization noise.
Referring now to FIG. 3, a 10 GBASE-T transmitter 20 having a pre-coder 18 is illustrated. An input signal ak is provided to a summing module 22, the addition module 22 generates a summed signal dk as will be described below. The signal dk is provided to a modulo operation module 24 where it is converted to a signal sk that has N-bits. Feedback of the signal sk is provided through a feedback filter 26 having a transfer function P(z). The output of the feedback filter 26 is provided to the addition module 22. Referring back to modulo operation module 24, the N-bit signal, sk is provided to the truncation module 28, which truncates the signal to an M-bit signal that is provided to the digital-to-analog converter 32 conversion to an analog signal. The digital-to-analog converter 32 illustrated in FIG. 3 may be implemented with Tomlinson-Harashima-Precode (THP). The approach illustrated in FIGS. 1-3 has quantization noise problems that degrade the performance of the communication system.